Fiona Knoll

Doctoral Research

  • Dimension Reduction Techniques via Johnson Lindenstrauss Transformations

Research Interests

  • Cryptography
    • Homomorphic Cryptography
    • Cloud Security and Side Channel Analysis
  • Coding Theory
    • Distributed Data Storage
    • Parallel Computing
  • Graph Theory
  • Mathematics and Music

Publications

  • Michael Burr, Shuhong Gao, Fiona Knoll. "On the Lower Bounds of Johnson-Lindenstrauss Transformation." In preparation.
  • Lin You, Fiona Knoll, Yue Mao, Shuhong Gao. "Practical Johnson-Lindenstrauss Transforms via Algebraic Geometry Codes." ICCAIRO 2017. Accepted.
  • Shuhong Gao, Fiona Knoll, Felice Mangianello, Gretchen Matthews "Codes for distributed storage from 3-regular graphs." Discrete Applied Mathematics, 229:82-89, 2017.
  • S. Hedetniemi, F. Knoll, R. Laskar. "Split Domination, Independence, and Irredundance in Graphs." Congressus Numerantium, 2016.
  • A. Grady, F. Knoll, R. Laskar, DJ Lipman. "Cycle Domination, Independence, and Irredundance in Graphs." Congressus Numerantium, 224:159-174, 2015.
  • A.Grady, F. Knoll, DJ Lipman. "Clique Independence, Domination, and Irredundance in Graphs." Congressus Numerantium, 223:193-198, 2015.

Conference Presentations

  • Joint Mathematics Meetings January 2017

  • Presented research on the bounds of Johnson-Lindenstrauss transformations.

  • 2016 Fall Central Sectional Meeting October 2016

  • Presented research on Johnson-Lindenstrauss transformations via Algebraic Geometry codes.

  • Southeastern International Conference on Combinatorics, Graph Theory, and Computing March 2016

  • Presented research on the graph theory concepts of split irredundance and split independence.

  • Joint Mathematics Meetings January 2016

  • Presented research on Johnson-Lindenstrauss transformations via Algebraic Geometry codes.

  • Association for Women in Mathematics Research Symposium April 2015

  • Presented a poster on Johnson-Lindenstrauss projection of high dimensional data.

  • Southeastern International Conference on Combinatorics, Graph Theory, and Computing March 2015

  • Presented research on an abstraction of domination chains, specifically domination chains concerning cycle independence graphs.